An uncountable Noetherian ring with free additive group

O’Neill, John D.

doi:10.1090/S0002-9939-1977-0450426-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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An uncountable Noetherian ring with free additive group
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by John D. O’Neill

Proc. Amer. Math. Soc. 66 (1977), 205-207

DOI: https://doi.org/10.1090/S0002-9939-1977-0450426-2

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Abstract:

An example is given of an uncountable Noetherian ring whose additive group is free. This answers a question posed indirectly by L. Fuchs.

References

László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
László Fuchs, Infinite abelian groups. Vol. II, Pure and Applied Mathematics. Vol. 36-II, Academic Press, New York-London, 1973. MR 0349869
Paul Hill, On the splitting of modules and abelian groups, Canadian J. Math. 26 (1974), 68–77. MR 338217, DOI 10.4153/CJM-1974-007-6